On some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm

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dc.creatorKleefeld, F.
dc.date2006-06-08
dc.date2006-06-15
dc.date.accessioned2026-07-07T10:43:00Z
dc.date.available2026-07-07T10:43:00Z
dc.descriptionA simple derivation of a meaningful, manifestly covariant inner product for real Klein-Gordon (KG) fields with positive semi-definite norm is provided which turns out - assuming a symmetric bilinear form - to be the real-KG-field limit of the inner product for complex KG fields reviewed by A. Mostafazadeh and F. Zamani in December, 2003, and February, 2006 (quant-ph/0312078, quant-ph/0602151, quant-ph/0602161). It is explicitly shown that the positive semi-definite norm associated with the derived inner product for real KG fields measures the number of active positive and negative energy Fourier modes of the real KG field on the relativistic mass shell. The very existence of an inner product with positive semi-definite norm for the considered real, i.e. neutral, KG fields shows that the metric operator entering the inner product does not contain the charge-conjugation operator. This observation sheds some additional light on the meaning of the C operator in the CPT inner product of PT-symmetric Quantum Mechanics defined by C.M. Bender, D.C. Brody and H.F. Jones.
dc.description8 pages, no figures; correction of obvious typos and marginal improvement of formulations
dc.identifierhttps://arxiv.org/abs/quant-ph/0606070
dc.identifierhttp://arxiv.org/abs/quant-ph/0606070
dc.identifierCzech.J.Phys.56:999-1006,2006
dc.identifierdoi:10.1007/s10582-006-0395-9
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/182148
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectHigh Energy Physics - Theory
dc.titleOn some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm
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